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作者：Dassios, Angelos
作者单位：University of London; London School Economics & Political Science
摘要：The purpose of this note is to obtain a representation of the distribution of the alpha-quantile of a process with stationary and independent increments as the sum of the supremum and the infimum of two rescaled independent copies of the process. This representation has already been proved for a Brownian motion. The proof is based on already known discrete time results.
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作者：Diaconis, P.; Saloff-Coste, L.
作者单位：Harvard University; Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：This is an expository paper on the use of logarithmic Sobolev inequalities for bounding rates of convergence of Markov chains on finite state spaces to their stationary distributions. Logarithmic Sobolev inequalities complement eigenvalue techniques and work for nonreversible chains in continuous time. Some aspects of the theory simplify considerably with finite state spaces and we are able to give a self-contained development. Examples of applications include the study of a Metropolis chain f...
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作者：Sadowsky, John S.
作者单位：Arizona State University; Arizona State University-Tempe
摘要：Importance sampling is a Monte Carlo technique where random data are sampled from an alternative sampling distribution and an unbiased estimator is obtained by likelihood ratio weighting. Here we consider estimation of large deviations probabilities via importance sampling. Previous works have shown, for certain special cases, that exponentially twisted distributions possess a strong asymptotic optimality property as a sampling distribution. The results of this paper unify and generalize the p...
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作者：Harrison, J. M.; Williams, J.
作者单位：Stanford University; University of California System; University of California San Diego
摘要：We consider a multiclass closed queueing network model analogous to the open network models of Rybko and Stolyar and of Lu and Kumar. The closed network has two single-server stations and a fixed customer population of size n. Customers are routed in cyclic fashion through four distinct classes, two of which are served at each station, and each server uses a preemptive-resume priority discipline. The service time distribution for each customer class is exponential, and attention is focused on ...
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作者：Kesten, Harry; Lee, Sungchul
作者单位：Cornell University; National University of Singapore
摘要：Let {X-i, 1 <= i < infinity} be i.i.d. with uniform distribution on [0, 1](d) and let M(X-1, . . . , X-n;alpha) be min{Sigma(e is an element of T') |e|(alpha); T' a spanning tree on {X-1, . . . , X-n;alpha) - EM(X-1, . . . , X-n}}. Then we show that for alpha > 0, [GRAPHIC] in distribution for some sigma(2)(alpha,d) > 0.
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作者：Bladt, Mogens
作者单位：Universidad Nacional Autonoma de Mexico
摘要：In this paper we consider the asymptotic time average variance of the actual waiting time of the PH/PH/1 queue. To this end Poisson's equation plays a major role, since the solution to Poisson's equation is shown to be intimately connected with the desired variance. We derive explicit solutions to Poisson's equation using phase-type methodology, and present some numerical examples.
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作者：Clancy, Damian
作者单位：University of Liverpool
摘要：We consider a stochastic model for the spread of an epidemic in a population split into m groups in which both infective and susceptible individuals are able to move between groups. Using a coupling argument similar to those applied to various other epidemic models by previous authors, we show that as the initial susceptible population becomes large, the process of infectives in this epidemic model converges to a multitype birth-and-death process with time-dependent birth rates. The behavior o...
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作者：Dai, J. G.
作者单位：University System of Georgia; Georgia Institute of Technology; University System of Georgia; Georgia Institute of Technology
摘要：This paper studies the instability of multiclass queueing networks. We prove that if a fluid limit model of the queueing network is weakly unstable, then the queueing network is unstable in the sense that the total number of customers in the queueing network diverges to in finity with probability 1 as time t -> infinity. Our result provides a converse to a recent result of Dai which states that a queueing network is positive Harris recurrent if a corresponding fluid limit model is stable. Exam...
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作者：Cvitanic, Jaksa; Ma, Jin
作者单位：Columbia University; Purdue University System; Purdue University
摘要：In the classical continuous-time financial market model, stock prices have been understood as solutions to linear stochastic differential equations, and an important problem to solve is the problem of hedging options (functions of the stock price values at the expiration date). In this paper we consider the hedging problem not only with a price model that is nonlinear, but also with coefficients of the price equations that can depend on the portfolio strategy and the wealth process of the hedg...
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作者：Burdzy, Krzysztof; Madrecki, Andrzej
作者单位：University of Washington; University of Washington Seattle; Wroclaw University of Science & Technology
摘要：We study an asymptotically 4-stable process. The main result is an Ito type formula.
